1 Sector-Specfc Techncal Change Susanto Basu, John Fernald, Jonas Fsher, and Mles Kmball 1 November 2013 Abstract: Theory mples that the economy responds dfferently to technology shocks that affect the producton of consumpton versus nvestment goods. We estmate ndustry-level technology nnovatons and use the nput-output tables to relax the typcal assumptons n the nvestment-specfc techncal change lterature assumptons that, we fnd, do not hold n the data. We fnd that nvestment-technology mprovements are sharply contractonary for hours, nvestment, consumpton, and output. Consumpton-technology mprovements, on the contrary, are generally expansonary. Thus, dsaggregatng technology shocks nto consumpton and nvestment-specfc changes yelds two shocks that both produce busness-cycle comovement, and also explan a large fracton of annual changes n GDP and ts components. Most of the responses we fnd are consstent wth the predctons of smple two-sector models wth stcky prces. JEL Codes: E32, O41, O47 Keywords: Investment-specfc techncal change, multsector growth models, busness cycles 1 Boston College and NBER, Federal Reserve Bank of San Francsco, Federal Reserve Bank of Chcago, and Unversty of Mchgan and NBER, respectvely. We thank Fasal Ahmed, Ttan Alon, Laure Glapa, Davd Thpphavong, Kun Natsuk, and, especally, Kyle Matoba and Stephane Wang for superb research assstance. We thank semnar partcpants at several nsttutons and conferences. The vews expressed n ths paper are those of the authors, and do not necessarly reflect the vews of anyone else afflated wth the Federal Reserve System.
2 I. Introducton What shocks drve busness cycles? At a mnmum, such shocks must move output, consumpton, nvestment and hours worked n the same drecton, as ths postve comovement s a defnng characterstc of busness cycles. Technology shocks are attractve canddates, because they can reproduce ths comovement n smple, general-equlbrum models of fluctuatons. But n the data, technology shocks dentfed usng restrctons from one-sector models do not produce postve comovement. In partcular, Gal (1999) and Basu, Fernald and Kmball (2006) fnd that technology shocks often rase output and consumpton, but lower hours worked. Revewng ths evdence, Francs and Ramey (2005) conclude the orgnal technology-drven busness cycle hypothess does appear to be dead. We revst the ssue of technology shocks and busness-cycle comovement because there s no consensus n the lterature on other shocks that could plausbly account for the bulk of the fluctuatons that we observe. (For example, monetary shocks produce the rght comovements, but are generally estmated to account for a very small fracton of economc volatlty.) Our goal s to see whether the conclusons about technology shocks reached earler mght be due to mposng the restrctons of a one-sector model of growth and fluctuatons n a world where they do not apply. If there are multple technologes, each affectng a dfferent type of good, mght t be the case that each type of shock ndvdually generates the proper comovements even though ther average does not? We frst show that our hypothess has a frm bass n economc theory. Theory tells us that the composton of technologcal change, n terms of the type of fnal good whose producton s affected, matters for the dynamcs of the economy s response to technology shocks. For example, we show that a shock to the technology for producng consumpton goods has no nterestng
3 3 busness-cycle effects n a standard RBC model. All of the dynamcs of hours and nvestment stressed by RBC theory come from shocks to the technology for producng nvestment goods. 2 In an open economy, terms-of-trade shocks affect the economy s ablty to provde consumpton and nvestment goods for fnal use, even f no domestc producer has had a change n technology. We then present a new and more robust method for estmatng sector-specfc techncal change. Exstng methods for nvestgatng the mportance of sector-specfc technology are based prmarly on relatve movements n the prce deflators for nvestment and consumpton goods, an approach poneered n an mportant paper by Greenwood, Hercowtz and Krusell (1997; henceforth GHK). Our evdence, n contrast, s based on an augmented growth-accountng approach, where we estmate technology change at a dsaggregated ndustry level and then use the nput-output tables to aggregate these changes. Our approach offers several advantages. Frst, we can relax and, ndeed, test many of the assumptons necessary for relatve-prce movements to correctly measure relatve changes n domestc technologcal change. For example, suppose dfferent producers have dfferent factor shares or face dfferent nput prces; or suppose markups change over tme. Then relatve prces do not properly measure relatve techncal change. 3 Second, we dscuss extensons to the open economy, where the ablty to mport and export means that relatve nvestment prces need not measure relatve technologes n terms of domestc producton. We vew our ablty to allow for dfferences n sectoral factor shares as the most mportant advantage of our method. All methods that use relatve prce changes to dentfy technology shocks (wth ether short- or long-run restrctons) requre that all fnal-use sectors have the same 2 Greenwood, Hercowtz and Krusell (2000) provde an nsghtful approach to busness-cycle modelng wth sector-specfc techncal change. However, they used a normalzaton for sector-specfc technology that dd not have a pure consumpton-augmentng shock, and thus dd not uncover ths neutralty result. 3 We can also test the orthogonalty restrctons used n the structural VAR approach of Fsher (2006), who also uses relatve prce data but wth a long-run restrcton.
4 4 factor shares. We are able to calculate these fnal-use shares usng our method, and fnd that they dffer sgnfcantly across sectors. Thus, one mportant concluson of our paper s that relatve prces cannot and should not be used to estmate nvestment-specfc techncal change. Applyng our method to sectoral US data, we fnd that consumpton-specfc and nvestment-specfc technology shocks have very dfferent economc effects. In partcular, consumpton-specfc technology mprovements are generally expansonary for all mportant busness-cycle varables (although the rse n hours worked s not statstcally sgnfcant, the pont estmates are postve and of the rght economc magntude). By contrast, nvestment-specfc technology mprovements are contractonary for all mportant busness-cycle varables, wth statstcally sgnfcant declnes n GDP, consumpton, hours worked, and even nvestment. Importantly, both shocks nduce postve comovement among the key busness-cycle varables, ncludng output, consumpton, nvestment and hours. Thus, the frst major fndng of the paper s to present a set of shocks that explan a sgnfcant fracton of GDP growth (more than 30 percent), whle explanng busness-cycle fluctuatons n key macro varables. As we show n the next secton, however, nether set of responses s consstent wth RBC theory. Clearly RBC theory would not predct a declne n GDP, consumpton, hours and, especally, nvestment followng an nvestment technology mprovement. Perhaps more surprsngly, the fact that hours and nvestment rse after a postve consumpton technology nvestment s also evdence aganst the RBC model. However, Basu, Fernald and Lu (2012) show that these responses are generally consstent wth the predctons of smple two-sector stcky-prce models. In conjuncton, the theory and emprcal work n our paper suggests that we need to revst several nfluental emprcal lteratures usng mult-sector economc models. For example, papers n the large lterature on the macroeconomc effects of technology shocks typcally examne the
5 5 responses of macroeconomc varables to aggregate measures of techncal change. 4 But f consumpton- and nvestment-specfc shocks are expected to have dfferent economc effects, aggregatng the two nto a sngle measure can ntroduce sgnfcant measurement error n an explanatory varable. To take another example, many papers follow the suggeston of Cochrane (1994) and take the consumpton-output rato to be a measure of permanent ncome relatve to current ncome. In a general-equlbrum model, the gap s usually due to (expected) changes n productvty. Rotemberg and Woodford (1996) use ths nterpretaton to fashon an emprcal crtque of RBC models by comparng the expected transtory changes n macroeconomc varables n the data to those predcted by a one-sector RBC model. But the correlaton between expected changes n consumpton, output and other varables can be qute dfferent dependng on whether the shock affects consumpton technology, nvestment technology, or both. Thus, t may be necessary to revst Rotemberg and Woodford s nfluental crtque by comparng the data to the predctons of mult-sector RBC models. Our approach to the data also forces us to thnk about the role of the open economy n economc fluctuatons. That s, our approach requres that we take a stand on the technology for producng net exports. Thus, we need to decde whether to take a narrow or broad vew of technology. The narrow vew s to say that technology s just somethng that shfts a domestc producton functon. We choose to take a broader vew, and defne technology from the consumpton possbltes fronter: At least n a neoclasscal model where there are stable preferences and no dstortons, technology s anythng that changes consumpton for gven levels of captal, nvestment and hours worked. Technology thus defned therefore ncorporates changes n 4 An excepton s Fsher (2006).
6 6 the terms of trade. It s clear, of course, that terms of trade changes do not shft domestc producton functons, and thus are not technology shocks n the narrow sense. 5 But t s also true that domestc technology shocks are not the only sources of changes n consumpton and welfare, even n a fully neoclasscal model. Understandng the behavor of consumpton n both the short and long run requres us to take an open-economy, mult-sector approach. The paper s structured as follows. After ths ntroducton, we provde a smple theoretcal example that llustrates that consumpton- and nvestment-specfc shocks should have very dfferent economc effects. Ths example motvates us to wrte down a macroeconomc model to gude our emprcal work. Specfcally, the model shows how to map from messy mcroeconomc producton and nternatonal trade data nto smple macroeconomc aggregates. We then dscuss the data, present results, and draw conclusons. II. Consumpton-Technology Neutralty The character of both growth and busness cycles depends on the sectoral dstrbuton of techncal change. In the neoclasscal growth model, captal accumulaton arses only f techncal change expands the possbltes for producng captal goods. Indeed, as shown by Kmball (1994), wth balanced growth, technology change that affects the consumpton-producng sector alone has no mpact on employment or captal accumulaton at all. Hence, the nature of growth s tghtly connected to the sectoral dstrbuton of techncal change. The response of a real busness cycle model economy to an exogenous technology shock also depends on the sectors of the economy t affects. Hours and nvestment responses to a pervasve, sector-neutral, postve technology shock are well understood. They follow from the ntertemporal substtuton of current lesure and consumpton for future consumpton. The 5 See Kehoe and Ruhl (2006).
7 7 household s wllng to do ths because of the hgh returns to workng and savng. These effects are amplfed when techncal change affects the nvestment sector alone, because current consumpton s even more expensve relatve to future consumpton n ths case (e.g., Fsher, 2007). Consumpton-sector shocks have smaller effects on ntertemporal substtuton and so have much less effect on decson rules. As Fsher (1994, 1997) and Kmball (1994) dscuss, f preferences are logarthmc, then the decson rules for nvestment and hours, as well as the allocaton of captal and labor across producng consumpton and nvestment goods, are nvarant to the stochastc process of consumpton-specfc technology. More generally, for preferences that* are consstent wth balanced growth, hours and nvestment and factor allocatons do not respond to a technology shock, f that shock s permanent, unantcpated, and affects only the consumpton sector. So the nature of busness cycles s also ted to the sectoral dstrbuton of techncal change. We now present a smple model to llustrate these ponts. We then dscuss other recent macroeconomc work that has focused on the fnal-goods sector n whch techncal change occurs. The emprcal evdence has been drawn almost exclusvely from aggregate data, wth heavy relance on relatve prces. Consder the two-sector closed-economy neoclasscal growth model. Suppose one sector produces consumpton goods C, the other sector produces nvestment goods, J. Both sectors produce output by combnng captal K and labor L wth the same functon F but separate Hcksneutral technology parameters, Z C and Z J. In partcular, consder the socal planner s problem for the followng problem, where vl ( t ) s a convex and s the deprecaton rate on captal: t max E [ln( C ) v( L )] 0 t0 t t Subject to: C Z F( K, L ); J Z G( K, L ) t Ct Ct Ct t Jt Jt Jt K K K ; L L L ; t Ct Jt t Ct Jt K J (1 ) K, K gven t1 t t 0
8 8 Ths setup appears n the recent lterature n varous places. For example, ths s a twosector verson of the model n Greenwood, Hercowtz, and Krusell (GHK, 1997); Whelan (2000) dscusses the mappng to GHK n greater detal. There are varous ways to normalze the technology shocks. For example, GHK defne Z J = Z C q, where q = Z J /Z C,. GHK label Z C as neutral technology and q as nvestment specfc, a labelng that has been wdely followed snce. A shock that rases Z C but leaves q unchanged s neutral n that both Z C and Z J ncrease equally. For the purposes of dscussng consumpton-technology neutralty, a dfferent normalzaton s more natural. In partcular, suppose we defne A = Z C /Z J as consumpton-specfc technology. Then the problem above can be expressed as a specal case of the followng problem, where we have made use of the assumpton of equal factor shares n the two sectors so there s a sngle aggregate resource constrant: t max E [ln( C ) v( L )] 0 t0 t t Subject to: C AX ; X J Z F( K, L) t t t t t t t t K J (1 ) K ; K gven t1 t t 0 X s an ndex of nputs devoted to consumpton (n the prevous example, t would correspond to the producton functon Z J F(K C, L C ). Snce X=C/A, and A corresponds (n the decentralzed equlbrum) to the relatve prce of nvestment to consumpton, we can nterpret X as consumpton n nvestment-goods unts (.e., nomnal consumpton deflated by the nvestment deflator). Ths s essentally the same approach taken by GHK, except that gven ther normalzaton they express everythng (nvestment and output, n partcular) n consumpton unts. Gven the logarthmc preferences for consumpton ths last problem can be expressed as:
9 9 max E t [ln( A) ln( X ) v( L )] 0 t0 t t t Subject to: X J Z F( K, L) t t t t t K J (1 ) K ; K gven t1 t t 0 Consumpton-technology neutralty follows drectly from ths expresson of the problem. In partcular, because ln(a) s an addtvely separable term, any stochastc process for A has no effect on the optmal decson rules for L, X, or J. They do not nduce captal-deepenng or any of the expected RBC effects; e.g., employment doesn t change. Consumpton jumps up, whch mmedately moves the economy to ts new steady state. 6 Consumpton shocks affect only real consumpton and the relatve prce of consumpton goods. In contrast, nvestment-sector technology shocks would have much more nterestng dynamcs. They nduce long-run captaldeepenng, and even n the short-run affect labor supply and nvestment dynamcs. Thus, consumpton-sector technology shocks are neutral. Ths consumpton-technology neutralty proposton has been mplct n two-sector formulatons for a long tme; the frst explct references we are aware of are Kmball (1994) and Fsher (1994). Nevertheless, t appears to be a lttle-known result. One reason s that the semnal work by Greenwood, Hercowtz, and Krusell (1997) used a dfferent normalzaton, as noted above; they focused on the response of the economy to nvestment specfc shocks. A shock to consumpton technology alone (leavng nvestment technology unchanged) would then nvolve a postve neutral shock, combned wth a negatve nvestment-specfc shock. 7 6 Kmball (1994) dscusses ths case further, as well as the extenson to Kng-Plosser-Rebelo (1988) preferences. 7 Equvalently, a postve shock to nvestment-specfc technology (wth neutral technology unchanged) or a postve shock to neutral technology (leavng nvestment-specfc technology unchanged) would both rase nvestmenttechnology n the two-sector formulaton, and hence would lead to dynamc responses n the frctonless model.
10 10 The theoretcal motvaton for studyng sectoral techncal change s bolstered by a nascent emprcal lterature. Most of ths lterature has followed the GHK normalzaton of neutral and nvestment specfc shocks. GHK used data on real equpment prces and argued that nvestment-specfc, not sector-neutral, techncal change, s the prmary source of economc growth, accountng for as much as 60% of per capta ncome growth. Cummns and Volante (2000) also fnd that nvestment-specfc techncal change s a major part of growth usng more recent data. Several papers also hghlght the potental role sector-specfc technology shocks n the busness cycle. Greenwood, Hercowtz and Huffman (1988) were the frst to consder nvestment-specfc shocks n a real busness cycle model. Other papers studyng nvestmentspecfc shocks wthn the context of fully-specfed models are Campbell (1998), Chrstano and Fsher (1998), Fsher (1997), and Greenwood, Hercowtz and Krusell (2000). These authors attrbute 30-70% of busness cycle varaton to permanent nvestment-specfc shocks. In the structural VAR lterature, Fsher (2006), extendng the framework used by Gal (1999) to the case of nvestment-specfc shocks, fnds that nvestment-specfc shocks explan 40-60% of the shortrun varaton n hours and output. 8 Ths pror work s based on a top-down measurement strategy that reles on nvestment and consumpton deflators (ether drectly from the BEA, or augmented wth equpment deflators from Gordon (1990), and Cummns-Volante (2002). Our paper contrbutes to the lterature by provdng new measures of sector-specfc techncal change based on ndustry-level data that, n prncple, are more robust. These new measures of techncal change can be used to assess the veracty of the exstng lterature s fndngs. The next secton descrbes the theoretcal framework underlyng our measurement. 8 Fsher s mpulse response functons look smlar to the subperod results n Gal, Lopez-Saldo, and Valles (2002), wth technology shocks reducng hours worked n the pre-1979 perod and rasng them thereafter.
11 11 III. Theoretcal Framework We now descrbe the theoretcal framework we use to dentfy sector-specfc technology shocks. Ths framework shows how to map from complcated ndustry-level data on producton and trade to key macroeconomc aggregates. Most mportantly t embodes the ndustry/commodty nput-output structure of US producton, ncludng the actvtes of exportng and mportng, and the fact that the same commodty can be produced domestcally and be mported. We assume only three domestcally produced fnal goods and homogeneous factor nputs, but the model s easly extended to accommodate the greater number of fnal goods and commodty-specfc factor nputs that we use n our emprcal work. In addton, here we assume perfect competton wth constant-returns-to-scale producton, but we consder the mplcatons of extensons to ths baselne n our emprcal work. 9 The remander of ths secton begns by descrbng the ntermedate nput economy whch maps drectly to our data. Next, we dscuss the fnal good economy that corresponds to the ntermedate nput economy. Thrd we show how to express the technologes and factor shares of the fnal good economy n terms of the technologes, factor shares and shares of ntermedate goods n gross output of the ntermedate nput economy. Intermedate Input Economy The economy comprses three fnal goods, consumpton, nvestment and exports, and commodtes whch are produced domestcally and can also be mported. Domestcally produced and mported commodtes must be combned to produce a usable commodty before they can be used as nputs to the producton of the fnal goods or as an ntermedate nput to the domestc 9 Not n ths draft, though.
12 12 producton of commodtes. Domestc producton of commodtes nvolves captal, labor and ntermedate nputs. Fnal goods are produced as constant elastcty of substtuton aggregates of the usable commodtes. There s a representatve agent who consumes the consumpton good, supples labor, owns the captal stock and engages n borrowng and lendng on nternatonal captal markets. Captal and labor are homogenous. Net exports, the terms-of-trade and the world nterest rate are exogenously gven n the model. We relax ths assumpton n our emprcal work. Compettve equlbrum allocatons are obtaned as the soluton to the followng plannng problem: s t t s s s= t max E UC (, L) Subject to: C C C J J J Ct = ( Y1 t,..., Y t) ; Jt = ( Y1 t,..., Y t) X X X X Xt ( Y1 t, Y2t..., Y t) ; N = X ( Y f / ToT ) t t t t Y = Z F ( K, L, M, M,, M ), = 1,..., d t t t t 1t 2t t d f Y = ( Y, Y ), =1,..., ; t t t C J X t jt t t t j=1 Y = M Y Y Y, = 1,..., K t = Kt; L t = L t K =(1 ) t1 Kt Jt; A =(1 ) t1 r At Xt; A0, K0 gven Here C, J, X and N denote the fnal goods consumpton, nvestment, gross exports and net exports;, = CJX,,, N F, = 1,..., and are constant-returns-to-scale producton functons; ToT t denotes the terms-of trade for mportng commodty ; d Y t and f Y t denote the domestc producton and mports of foregn produced commodty ; Z t s the exogenous
13 13 technology for producng commodty ; Y t s the producton of usable commodty ; M jt denotes ntermedate nput of commodty j used n the producton of commodty ; K t and L t are captal and labor nputs to the producton of domestc commodtes; K t and L t are the aggregate stocks of captal and labor;. and r s the world nterest and A t s net foregn lendng (whch evolves exogenously because net exports N s exogenous.) The one unusual thng about net exports N as a fnal good s that t can be negatve. When net exports are negatve, the perspectve taken here s that mports can be obtaned ether by means of the export commodty or by means of an electronc credt, A, stated n terms of unts of the export commodty. Thus, negatve net exports are n unts of the export commodty and represent the amount of electronc credts treated as equvalent to unts of the export commodty that domestc buyers of mports have been lent. Ths perspectve s valuable because there s only one aggregate export commodty, but many types of mports that the model keeps track of. 10 Because the model condtons on the tme path of net exports, t s not essental to keep track of the foregn debt. 11 Snce keepng track of the foregn debt s not central to the model here, for convenence, one can thnk of the foregn debt as beng stated n terms of unts of the export commodty. Fnal Good Economy Our aggregaton converts the commodty TFPs Z t nto fnal good TFP. The aggregaton s exact for the case where all the producton functons are Cobb-Douglas and yelds growth rates for TFP that are correct up to second-order approxmatons of the producton functons. To be clear on 10 Everythng would be equvalent f net exports were expressed n terms of any partcular mported commodty, but t would be necessary to pck one, snce dfferental changes n the prces of dfferent mported commodtes makes them non-equvalent, fnancally. 11 That s, the man reason one would need to keep track of foregn debt s to determne the tme path of net exports. It s part of the relevant ntertemporal budget constrant n that determnaton.
14 14 what our aggregaton acheves, we now state the socal planners problem n terms of fnal goods only. Ths problem yelds dentcal allocatons for the fnal goods and factor nputs f the producton functons are all Cobb-Douglas. The reduced form plannng problem n terms of fnal goods only s: s t t s s s= t max E UC (, L) Subject to: C C C C C Z G ( K, L ); J ZG J J ( K J, L J ) t t t t t t t t N N N X N Z G ( K, L ); K = K C K J K N t t t t t t t t L L L L ; K =(1 ) 1 K J = C J N t t t t t t t A =(1 ) t1 r At Nt; A0, K 0 gven As before the terms-of-trade, net exports and the world nterest rate are assumed n the model to be exogenous. Note that f we elmnate the nternatonal sector then ths model would reduce to the two-sector model dscussed n Secton II except that here the producton functons are allowed to dffer across sectors. The thrd constrant shows the producton functon for producng net exports. Our treatment of net exports s new and so deserves some dscusson. When net exports are negatve, the captal and labor nputs are also negatve. 12 Ths arses because consumpton and nvestment goods are produced usng mported commodtes and when there s a negatve trade balance some of these commodtes are obtaned wth the electronc credts assocated wth nternatonal borrowng mentoned above, n addton to the captal and labor used to produce the exported commodtes. In 12 Under constant returns the mnus ones multplyng each factor nput convert to a mnus one n front of the producton functon. Ths avods rasng negatve numbers to non-nteger powers and havng to deal wth magnary numbers.
15 15 ths case, the captal and labor allocated to producng consumpton and nvestment ncludes the captal and labor that s equvalent n value to the electronc credts. Consequently ths captal and labor must be subtracted from the correspondng factor nput resource constrants. Wth balanced trade the quantty of captal and labor used to produce the exported commodtes s suffcent to acqure all the mported commodtes that end up n the fnal goods so that the captal and labor nputs to the net export technology are equal to zero. Wth a postve trade balance the captal and labor employed n the economy exceed the amount necessary to produce consumpton and nvestment and so captal and labor allocated to net exports are postve, reflectng the exports produced to acqure net foregn assets. Aggregatng the Fnal Good Economy from the Intermedate Input Economy C The fnal-good sector-specfc technologes Z, t J Z t and N Z t are the focus of our emprcal work. These varables can be expressed as weghted averages of domestc commodty TFP and terms-of-trade where the weghts depend on the shares of ntermedate nputs and trade n gross output. Factor nputs and factor shares n the producton of the fnal goods are smlarly defned share-weghted averages of factor shares and commodty shares assocated wth fnal goods producton. GDP n ths economy s measured usng the standard chan aggregaton wth fnal goods prces derved from the Lagrange multplers assocated wth the fnal good constrants n the plannng problem. The appendx descrbes the aggregaton from the model wth ntermedate goods and fnal goods to the model wth fnal goods only n detal; here we focus on the ntuton. To buld ntuton nto the nature of the aggregaton t s helpful to smplfy the underlyng ntermedate nput model to exclude the foregn trade sector. In ths closed economy model, consder the producton of a fnal commodty that s useable for consumpton or nvestment (for
16 16 example, a car) fnal Y. That commodty s a functon of all the captal and labor that, drectly or ndrectly, went nto producng t, and satsfes Y constant Z K N, (1) jajk 1 jajk fnal fnal j j where each a K s captal s share n the gross output producton functon for commodty and the j are the elements of the matrx gven by 1 ( I B). In ths last expresson I denotes the dentfy matrx and B s a matrx comprsng elements b j whch equal the ntermedate nput share of commodty j n the gross output producton functon for commodty. In equaton (1), K and L ncludes the captal and labor that was drectly used to produce a car, as well as the captal and labor that was used to produce the steel for the car, and the captal and labor used to extract ron ore to produce that steel. The mplct factor shares the exponents n the equaton account for the factor shares n auto producton, steel, and ron mnng. The term Z fnal aggregates the technologes correspondng to gross output of commodty j to yeld the technology for producng usable commodty. Specfcally Z fnal j Z j j The technology for a gven fnal good s then obtaned as the weghted average of the usable commodty technologes where the weghts are gven by the share of each usable commodty n value added of the fnal good. Ths follows from the fact that the fnal goods are constant-returnsto-scale aggregators of the usable commodtes. For example, n the Cobb-Douglas case the consumpton good technology s gven by C T ln Z bc ln Z. (2)
17 17 The technology for producng consumpton, Z C, depends on the column vector of underlyng commodty technology shocks Z as weghted by the nput-output table to get the usable commodty technologes and then weghted agan by the column vector of usable commodty shares of consumpton, b C. These usable commodty shares correspond to the shares of usable commodtes n the consumpton good aggregator 1C are smlarly obtaned as C. The captal and labor shares n C G, C and C C T and 1, T b C K b C N where K and N are vectors of captal and labor shares n commodty producton. Snce t s crucal to our measurement of fnal good technologes and factor shares, t s helpful to dscuss the matrx further. Consder the effects of an nnovaton to the vector of commodty technologes, Z. Frst, the vector Z gves the drect effect of commodty-level nnovatons on the dfferent commodty outputs. Second, the extra output of each commodty ncreases ts use proportonately as an ntermedate nput nto other commodtes; ths second-round effect s BZ. These second round effects on the quantty of each commodty yeld a thrd-round effect of 2 B Z and so on. In the end, as the technologcal mprovements n the producton of each commodty repeatedly work ther way through the nput-output matrx, there s an nput-output multpler of 2 3 I B B B, whch s equvalent to ( I ) 1 B and therefore also. A smlar logc explans the factor shares n the producton of the usable commodtes. For example, the vector of captal shares for the vertcally ntegrated producton of each usable commodty s gven by the vector, 2 3 ak [ I B B B...] ak
18 18 where ak s the vector of captal shares n the drect producton of commodty. The captal share for the vertcally-ntegrated producton of a commodty s the captal share for the drect producton of that commodty, plus the contrbuton from the captal shares of the materals needed to produce that commodty (the term n the expanson nvolvng B), plus the contrbuton from the materals needed to make those materals (the term n the expanson nvolvng B 2, and so on. Addng back the trade sector requres that we adjust the matrx B to address the addton of exports and the fact that fnal goods comprse both domestcally and foregn produced commodtes. These changes complcate the dervaton of but do not change the logc of the aggregaton. The man change to our measurement s to ntroduce the terms-of-trade nto the measurement of the fnal good technologes and factor shares. The terms-of-trade enter because we have modeled mports as ntermedate goods used to produce the fnal goods and the terms-of-trade are the technology for producng mports from exports. 13 Detals are n the appendx. Havng derved fnal good technologes t s useful to see how they compare to other measures n the lterature. Greenwood, Hercowtz and Krusell (2003) propose measurng the technology for producng nvestment goods relatve to that for producng consumpton goods usng the prce of nvestment goods relatve to consumpton goods and ths practce s common n the New Keynesan DSGE lterature. Smlarly, Fsher (2006) proposes dentfyng the dynamc response to the relatve technology usng the assumpton that only a shock to the relatve technology has a long run mpact on the relatve prce. In the appendx we derve a detaled 13 Of course, whle terms of trade shocks functon theoretcally just lke technology shocks, ther econometrc propertes wll be much dfferent. Terms of trade are lkely to be much closer to statonary, and are also lkely to be more radcally endogenous than technology schocks proper.
19 19 expresson showng that dfferences and sales taxes and share-weghted factor prces drve a wedge between relatve technologes and relatve fnal-goods prces. To buld ntuton nto the underlyng sources of that wedge t s helpful to consder the frst order condtons for labor and captal n the consumpton and nvestment sectors under the addtonal assumptons that factor nputs are heterogenous and fnal goods are subject to excse taxes. At any gven date, these frst order condtons can be wrtten C 1 C C 1 C J C C = 1 J 1 J J J C J J P Z R W P Z R W (3) where P C and P J are market prces, C and J are excse taxes, R C and captal, W C and dfferences we have W J are wage rates, and C and R J are rental prces of J are captal shares n producton. In log frst dp dp = dz dz dr (1 ) dw dr (1 ) dw d d (4) C J J C C C C C J J J J C J Clearly, at any pont n tme, unless factor shares and growth rates of taxes and factor prces are all dentcal then relatve prces and relatve technologes wll not be equal. If we add mperfect competton to the model then there s an addtonal wedge due to dfferences n the growth rates of mark-ups. Ths makes t clear that the conventon of equatng relatve prces wth relatve technologes at each pont n tme can be problematc. Our measurement s not subject to ths drawback. Note however, that as long as there are no permanent shocks to the wedges, that In the context of our model, one can show that f we aggregate accordng to equaton ( ) and use standard commodty-level TFP resduals (wthout controls for utlzaton or non-constant returns to scale), then relatve fnal-goods prces and relatve fnal-use TFP are related by the followng dentty:
20 Dom Dom,Producer dtfpj dtfpc dpc dpj ( bj bc)( I B) skdr sldw ( bj bc)( I B) dp dp Relatve prce + Factor-Prce Wedge Tax Wedge In the equaton, ( b b ) s a row vector for a gven year of commodty-specfc shares n J C fnal nvestment versus consumpton; a dr a dw s a column vector of commodty-specfc K share-weghted nput prce growth (where only domestc commodtes have non-zero entres); L smlarly, dp Dom dp Dom,Producer s a column vector of the dfference between prce pad by a purchaser and the prce receved by a producer. 14 IV. Data We use the KLEM dataset produced by Dale Jorgenson and hs collaborators, along wth the underlyng nput-output data. 15 The man vntage of data runs from , but we have merged them wth an earler vntage of Jorgenson data back to The dataset provdes consstent ndustry output and nputs as well as commodty fnal-use data for 35 ndustres/commodtes. (The dataset has the full nput-output use matrx only back to 1960; the so-called make table s avalable only back to 1977.) 16 ) The Jorgenson data offer several key advantages. Frst, they provde a unfed dataset that allows for productvty analyss by provdng annual data on gross output and nputs of captal, labor, and ntermedates. Second, the productvty data are ntegrated wth annual nput-output data that are measured on a consstent bass. The I-O data nclude not just ntermedate-nput flows 14 For ths equaton to hold as an dentty n the data, we need to allow fnal-use shares, the nput-output matrx B, and factor shares to vary perod-by-perod. Otherwse, ths s only an approxmaton. In the results, we show ths decomposton usng perod-by-perod shares. 15 The dataset updates Jorgenson, Gollop, and Fraumen (1987). We thank Dale Jorgenson as well as Barbara Fraumen, Mun Ho, and Kevn Stroh for helpful conversatons about the data. Jon Samuels helped tremendously wth data avalablty. The man data are avalable at (accessed Aprl 26, 2010). 16 The orgnal data source for nput-output and ndustry gross output data s generally the Bureau of Labor Statstcs whch has, for a long tme, produced annual versons of both nomnal and real (chaned) I-O tables. (The current vntage of data from the BLS Empoyment Projectons Program s avalable at (accessed Aprl 26, 2010).